Stationary random graphs on Z with prescribed iid
degrees and finite mean connections
Maria Deijfen, Stockholm University
Johan Jonasson, Chalmers University
Abstract
Let F be a probability distribution with support on
the non-negative integers. A model is proposed for generating
stationary simple graphs on Z with degree distribution
F and it is shown for this model that the expected total length
of all edges at a given vertex is finite if F has finite second
moment. It is not hard to see that any stationary model for
generating simple graphs on Z will give infinite mean
for the total edge length per vertex if F does not have finite
second moment. Hence, finite second moment of F is a necessary
and sufficient condition for the existence of a model with finite
mean total edge length.
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